1. Calculate y³ $ £ (-2² - sinz) dz + ( + v) ds. + dx dy, 3 3 where C is the circle of radius 1 centered at (0,0) oriented counterclockwise.

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Q: [25] Find the general solutions of 2y" + 8y' = 5 cot(2t).

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Q: Calculate the iterated integral integral [[ ³³√² + y^'dady. 0

A: That is evaluate ∫x3x4+y4dx .To evaluate this put the substitution x4+y4=z⟹4x3dx=dz…

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Q: (a) f: Z→ Z where f(x) = - -2 x+1 X- (b) f: RR where f(x) = [2x]. if x ≥ 5 if x ≤ 4 (c) f: A B where…

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Q: Find the values of a such that det (² 3-x 2 3-x 4 1 -1 -1-x = 0.

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Q: 4) Consider the following Riccati-type nonlinear differential equation: dy dx Guess the particular…

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Q: M J d -X(t) dt [3] 4. 1x0-13x0, = X(t), X(0) = 8.

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Q: TRANSCRIBE THE FOLLOWING TEXT IN DIGITAL FORMAT

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Q: a) what (seriz = cosz ; are the residues of IT csc(Tz) Cs 650 3 = गर्नेछ ) sin

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Q: B = ( and c = ([ C TB [M]B 0 -1 0 1] 0 1 0 for the vector space V of upper triangular 2 × 2…

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Q: Find the Laplace transform of the function given by f(t) = 3t if t ≤ 4 and f(t) = 12 if t > 4. F(s)…

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Q: Find L" 25 £= { 15 715) (5+2)) fo (5+1₁)

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Q: Let f: R² → R be defined by f((x, y)) = 7x - 5y. Is f a linear transformation? a. f((x₁, y₁) + (x2,…

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Q: Read the example in the photos, concerning the limit of the sequence (1/n). For this example: give…

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Q: (2) Let f(x) = x³ - 2x, find Ay and dy for x = 1 and Ax = dx = 0.1. (A) Ay = f(1.1) - f(1) = -0.869…

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Q: Proofs Task 4 (portfolio). Let an be a sequence decreasing to zero. Prove that En-1(-1)"an…

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Q: 2. Find the Laplace transform of the following function: 0 ≤ t 4. f(t) = 0, t², 0.

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